In January 1958, Charles Starkweather, a 20 year-old from Lincoln in Nebraska, and Caril Fugate, his 14-year-old girlfriend, embarked on a two-month killing spree that would result in the deaths of 10 people. Starkweather's first victims were Fugate's mother, stepfather and two-year-old sister. The couple hid the bodies, then holed up in Fugate's family home, discouraging visitors with a note pinned to the door that read: "Stay a Way Every Body is sick with the Flue."

When a relative grew suspicious and called the police, the couple fled – so beginning a deadly adventure that by turns mesmerised and appalled the American media and public. They were eventually captured in Douglas, Wyoming. Starkweather went to the electric chair in 1959 and Fugate began an 18-year sentence in Nebraska Correctional Centre for Women. She now lives in Michigan under an assumed name, and has never remarried, nor spoken of Starkweather or her part in the killings.

Long after the event, the couple's exploits continue to capture the American imagination. In 1973, Terrence Malick directed the disturbingly powerful Badlands, his debut feature film based on the murders and starring Sissy Spacek and Martin Sheen. In 1994, amid much controversy over its gratuitous violence, Oliver Stone's Natural Born Killers was released, another take on the same dark legend. In 1982, Bruce Springsteen released his album Nebraska, the title song of which begins: "Saw her standing on her front lawn / Just a-twirlin' her baton / Me and her went for a ride, sir, and 10 innocent people died / From the town of Lincoln, Nebraska, with a sawn-off .4-10 on my lap / To the badlands of Wyoming, I killed everything in my path."

In 1990, Sonic Youth released Goo, an album with a cover illustration by Raymond Pettibon featuring a cool couple in a car with the words: "I stole my sister's boyfriend. It was all whirlwind, heat and flash. Within a week, we killed our parents and hit the road."

Now comes Redheaded Peckerwood, a strange and beautiful photobook by Christian Patterson, a young photographer from Brooklyn. (The title refers to a derisory term coined by Southern black people to refer to poor whites from rural neighbourhoods, such as Starkweather and Fugate.) Fifty years after the event, Patterson followed the trail of Starkweather and Fugate across Nebraska and into Wyoming, his magpie eye picking out landscapes, buildings, woods, wastegrounds and darkly suggestive interiors. On the way, he visited the murder sites and the neighbourhoods of the killers and their victims, discovered personal letters and official documents pertaining to the case and trawled the archives of local papers such as the Lincoln Journal Star for first-hand accounts of the trial. He talked to police officers, local people, drifters and strangers he met in bars and coffee houses. The result is a unique photobook-cum-archive, a kind of impressionist visual narrative whose subtext is Patterson's own obsession with the couple and their dark mythology, an obsession that began when he watched Badlands for the first time in 2004.

"In Redheaded Peckerwood," writes Luc Sante in his essay for the book, "Christian Patterson is working out something that hasn't been done much before, if ever: a kind of subjective documentary photography of the historical past. That requires that the individual pictures be true, as close as possible to the physical details as historically established, while remaining ambiguous and unsettling …"

Chilling memento ... Patterson found the couple's stuffed toy at one of the murder sites

In a talk that Patterson gave on the book at Rough Trade East in London a few weeks ago, he spoke of the influence of the 1930s Crime Dossier series of books created by Dennis Wheatley and the art historian JG Links. The books went for an unconventional interactive approach, encouraging the reader to decipher the mystery though a series of clues – letters, documents, photographs – contained in cardboard folders that looked like police files. In Redheaded Peckerwood, the narrative is altogether more postmodern. For instance, some of the settings are actual, others symbolic. An ominous-looking house photographed at night belongs to one of Fugate's neighbours (her family home was demolished decades ago). A grey and ragged stuffed-toy dog is placed against a pink background, its tackiness emphasised. This was the gift Starkweather intended for Fugate – but the store owner, Robert Colvert, refused his credit. Colvert was shot dead by Starkweather on 30 November 1957, seven weeks before he set off on his epic killing spree with Fugate. Patterson found the ragged toy in the remains of one of the murder sites.

"Murder charges everything it touches," writes Sante. "Every blurred photo, scrap of writing, wadded rag and broken comb … things you'd never look at twice in any other context … takes on imminence with its association with violent death." This, then, is a book of testimony and suggestion; a murder mystery that offers no answers, only more clues, possibilities and interpretations. It looks back across the decades at a casually murderous saga that still eludes understanding and continues to fascinate. It brings to mind Springsteen's Nebraska song lyrics, in the voice of Charles Starkweather: "They wanted to know why I did what I did / Well, sir, I guess there's just a meanness in this world."